Related papers: Random cover times using the Poisson cylinder proc…
This article proves that, in terms of local times, the rescaled and recentered cover times of finite subsets of the discrete cylinder by simple random walk converge in law to the Gumbel distribution, as the cardinality of the set goes to…
Given a compact planar region $A$, let $\tau_A$ be the (random) time it takes for the Johnson-Mehl tessellation of $A$ to be complete, i.e. the time it takes for $A$ to be fully covered by a spatial birth-growth process in $A$ with seeds…
Random union sets $Z$ associated with stationary Poisson processes of $k$-cylinders in $\mathbb{R}^d$ are considered. Under general conditions on the typical cylinder base a concentration inequality for the volume of $Z$ restricted to a…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
In this paper we study the quenched distributions of hitting times for a class of random dynamical systems. We prove that hitting times to dynamically defined cylinders converge to a Poisson point process under the law of random equivariant…
Motivated by peer-to-peer telecommunication, we study a dynamic Boolean model. We define a Poisson number of random lines through the $(d-1)$-dimensional base of a $d$-dimensional unit cube and dilate them to define cylinders. Letting…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
In this article, we study a covering process of the discrete one-dimensional torus that uses connected arcs of random sizes in the covering. More precisely, fix a distribution \mu on \mathbb{N}, and for every n\geq 1 we will cover the torus…
We consider an ergodic process on finitely many states, with positive entropy. Our first main result asserts that the distribution function of the normalized waiting time for the first visit to a small (i.e., over a long block) cylinder set…
In this paper we study Poisson processes of so-called "fat" cylinders in hyperbolic space. As our main result we show that this model undergoes a percolation phase transition. We prove this by establishing a novel link between the fat…
In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…
We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…
We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard polynomials and the Poisson distribution. We also introduce a rather novel permutation…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall.…
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…